Question

lim (x^10-1024)/(x-2) x=2

Answer 1

lim (x^10 -1024)/(x-2)
x→2
= lim (x^10 - 2^10)/(x-2)
x→2
= 10 *2^9
=5120
here we used
lim ( x^n - a^n)/ (x-a) =n*a^(n-1)
x→a

Answer 2

On solving the given problem:

$\lim \frac{x^{10}-1024}{x-2} = 5120$

Given:

$\lim \frac{x^{10}-1024}{x-2}, \ x=2$

Solution:

The full form of LIM is limit. The LIM tells us how the function should look like and is should be how when you get a point from it.

$\lim \frac{x^{10}-1024}{x-2}$

By taking power value for 1024, we get,

$=\lim \frac{\left(x^{10}-2^{10}\right)}{x-2} \rightarrow 1$

By using the formula given below, in the equation in 1, we get,

$\frac{x^{n}-a^{n}}{x-a}=\mathrm{na}^{\mathrm{n}-1}$

$=10 \times 2^{10-1}$

$=10 \times 2^{9}$

$\Rightarrow \lim \frac{x^{10}-1024}{x-2}=5120$